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The quadratic spin squeezing operators

Pradyumna K. Pathak, Ram Narayan Deb, N. Nayak, Binayak Dutta-Roy

Published Aug 5, 2013• 6 citations
OpenAlex

Abstract

Abstract. We discuss generic spin squeezing operators (quadratic in angular momentum operators) capable of squeezing out quantum mechanical noise from a system of two-level atoms (spins) in a coherent state. Such systems have been considered by Kitagawa and Ueda (Refs. 2) in this context and a Hamiltonian of this nature governs the Lipkin model (Ref. 14) which is relevant to nuclear physics.

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We consider a system of $N$ two-level atoms (spins) interacting with the radiation field in a dispersive but high-$Q$ cavity. Under an adiabatic condition, the interaction Hamiltonian reduces to a function of spin operators which is capable of producing spin squeezing. For a bipartite system $(N=2)$, the expressions for spin squeezing get very simple, giving a clear indication of close to 100% noise reduction. We analyse this squeezing as a measure of bipartite entanglement.

Physical Review A•May 17, 2006•29 citations
Abstract. We discuss generic spin squeezing operators (quadratic in angular momentum operators) capable of squeezing out quantum mechanical noise from a system of two-level atoms (spins) in a coherent state. Such systems have been considered by Kitagawa and Ueda (Refs. 2) in this context and a Hamiltonian of this nature governs the Lipkin model (Ref. 14) which is relevant to nuclear physics.
We study the generation of spin squeezing by the repeated action of the angular momentum (Dicke) lowering operator on an atomic coherent state prepared for a collection of NNN two-level atoms or ions. The atoms or ions of the atomic coherent state are not entangled, but the action of the lowering operator (or similarly of the raising operator) generates entanglement among the atoms, and spin squeezing occurs for some ranges of the relevant parameter. Spin squeezing in a collection of two-level atoms or ions is of importance for precision spectroscopy. We discuss methods by which our spin-squeezed states could be generated in the contexts of cavity QED and trapped ions.
Spin squeezing is vitally important in quantum metrology and quantum information science. The noise reduction resulting from spin squeezing can surpass the standard quantum limit and even reach the Heisenberg limit (HL) in some special circumstances. However, systems that can reach the HL are very limited. Here, we study the spin squeezing in atomic systems with a generic form of the quadratic collective-spin interaction, which can be described by the Lipkin-Meshkov-Glick model. We find that the squeezing properties are determined by the initial states and the anisotropic parameters. Moreover, we propose a pulse rotation scheme to transform the model into a two-axis twisting model with Heisenberg-limited spin squeezing. Our study paves the way for reaching HL in a broad variety of systems.
Spin squeezing via atom-field interactions is considered within the context of the Tavis-Cummings model. An ensemble of N two-level atoms interacts with a quantized cavity field. For all the atoms initially in their ground states, it is shown that spin squeezing of both the atoms and the field can be achieved provided the initial state of the cavity field has coherence between number states differing by 2. Most of the discussion is restricted to the case of a cavity field initially in a coherent state, but initial squeezed states for the field are also discussed. Optimal conditions for obtaining squeezing are obtained. An analytic solution is found that is valid in the limit that the number of atoms is much greater than unity and is also much larger than the average number of photons, ${\ensuremath{\alpha}}^{2},$ initially in the coherent state of the cavity field. In this limit, the degree of spin squeezing increases with increasing $\ensuremath{\alpha},$ even though the field more closely resembles a classical field for which no spin squeezing could be achieved.
Spin squeezing in collective atomic ensembles enables quantum-enhanced metrology by reducing noise below the standard quantum limit through nonlinear interactions. Extending the one-axis and two-axis twisting paradigms of Kitagawa and Ueda, we introduce a general class of three-axis spin squeezed states within the anisotropic Lipkin-Meshkov-Glick model. The model features direction-dependent quadratic couplings that interpolate between uniaxial and biaxial regimes and can be interpreted as an asymmetric quantum rotor. Using semiclassical dynamics, Majorana representations, and Husimi-Q distributions, we analyze the structure and metrological properties of the resulting states. The three-axis framework reproduces the known N^(-2/3) scaling of one-axis twisting and the Heisenberg-limited N^(-1) scaling of two-axis twisting, while allowing additional tunability and enhanced entanglement generation in low-spin systems. We further show that tuning the anisotropy parameters induces ground-state and excited-state quantum phase transitions, including a second-order transition associated with level clustering and critical dynamics. These results unify spin squeezing, quantum criticality, and rotor analogies, and suggest implementations in Rydberg arrays and cavity-QED platforms for precision sensing and quantum simulation.
We consider a system of NNN two-level atoms (spins) interacting with the radiation field in a dispersive but high-QQQ cavity. Under an adiabatic condition, the interaction Hamiltonian reduces to a function of spin operators which is capable of producing spin squeezing. For a bipartite system (N=2)(N=2)(N=2), the expressions for spin squeezing get very simple, giving a clear indication of close to 100% noise reduction. We analyse this squeezing as a measure of bipartite entanglement.